\(\int x^m \text {Chi}(a+b x)^2 \, dx\) [93]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int x^m \text {Chi}(a+b x)^2 \, dx=\text {Int}\left (x^m \text {Chi}(a+b x)^2,x\right ) \]

[Out]

CannotIntegrate(x^m*Chi(b*x+a)^2,x)

Rubi [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int x^m \text {Chi}(a+b x)^2 \, dx=\int x^m \text {Chi}(a+b x)^2 \, dx \]

[In]

Int[x^m*CoshIntegral[a + b*x]^2,x]

[Out]

Defer[Int][x^m*CoshIntegral[a + b*x]^2, x]

Rubi steps \begin{align*} \text {integral}& = \int x^m \text {Chi}(a+b x)^2 \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 2.41 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {Chi}(a+b x)^2 \, dx=\int x^m \text {Chi}(a+b x)^2 \, dx \]

[In]

Integrate[x^m*CoshIntegral[a + b*x]^2,x]

[Out]

Integrate[x^m*CoshIntegral[a + b*x]^2, x]

Maple [N/A] (verified)

Not integrable

Time = 0.22 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00

\[\int x^{m} \operatorname {Chi}\left (b x +a \right )^{2}d x\]

[In]

int(x^m*Chi(b*x+a)^2,x)

[Out]

int(x^m*Chi(b*x+a)^2,x)

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {Chi}(a+b x)^2 \, dx=\int { x^{m} {\rm Chi}\left (b x + a\right )^{2} \,d x } \]

[In]

integrate(x^m*Chi(b*x+a)^2,x, algorithm="fricas")

[Out]

integral(x^m*cosh_integral(b*x + a)^2, x)

Sympy [N/A]

Not integrable

Time = 1.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \text {Chi}(a+b x)^2 \, dx=\int x^{m} \operatorname {Chi}^{2}\left (a + b x\right )\, dx \]

[In]

integrate(x**m*Chi(b*x+a)**2,x)

[Out]

Integral(x**m*Chi(a + b*x)**2, x)

Maxima [N/A]

Not integrable

Time = 0.21 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {Chi}(a+b x)^2 \, dx=\int { x^{m} {\rm Chi}\left (b x + a\right )^{2} \,d x } \]

[In]

integrate(x^m*Chi(b*x+a)^2,x, algorithm="maxima")

[Out]

integrate(x^m*Chi(b*x + a)^2, x)

Giac [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {Chi}(a+b x)^2 \, dx=\int { x^{m} {\rm Chi}\left (b x + a\right )^{2} \,d x } \]

[In]

integrate(x^m*Chi(b*x+a)^2,x, algorithm="giac")

[Out]

integrate(x^m*Chi(b*x + a)^2, x)

Mupad [N/A]

Not integrable

Time = 4.79 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {Chi}(a+b x)^2 \, dx=\int x^m\,{\mathrm {coshint}\left (a+b\,x\right )}^2 \,d x \]

[In]

int(x^m*coshint(a + b*x)^2,x)

[Out]

int(x^m*coshint(a + b*x)^2, x)